Model Updating Method Based on Kriging Model for Structural Dynamics

Hong Yin,Pan Cui,Chenghao Yang,Kangli Dong,Jingjing Ma,Zhenrui Peng

doi:10.1155/2019/8086024

Abstract

Model updating in structural dynamics has attracted much attention in recent decades. And high computational cost is frequently encountered during model updating. Surrogate model has attracted considerable attention for saving computational cost in finite element model updating (FEMU). In this study, a model updating method using frequency response function (FRF) based on Kriging model is proposed. The optimal excitation point is selected by using modal participation criterion. Initial sample points are chosen via design of experiment (DOE), and Kriging model is built using the corresponding acceleration frequency response functions. Then, Kriging model is improved via new sample points using mean square error (MSE) criterion and is used to replace the finite element model to participate in optimization. Cuckoo algorithm is used to obtain the updating parameters, where the objective function with the minimum frequency response deviation is constructed. And the proposed method is applied to a plane truss model FEMU, and the results are compared with those by the second-order response surface model (RSM) and the radial basis function model (RBF). The analysis results showed that the proposed method has good accuracy and high computational efficiency; errors of updating parameters are less than 0.2%; damage identification is with high precision. After updating, the curves of real and imaginary parts of acceleration FRF are in good agreement with the real ones.

Highlights

Model updating in structural dynamics has attracted much attention in recent decades
Initial sample points are chosen via design of experiment (DOE), and Kriging model is built using the corresponding acceleration frequency response functions. en, Kriging model is improved via new sample points using mean square error (MSE) criterion and is used to replace the finite element model to participate in optimization
The proposed method is applied to a plane truss model finite element model updating (FEMU), and the results are compared with those by the second-order response surface model (RSM) and the radial basis function model (RBF). e analysis results showed that the proposed method has good accuracy and high computational efficiency; errors of updating parameters are less than 0.2%; damage identification is with high precision

Summary

Kriging Model

Kriging model is considered as the best linear unbiased estimation to the real computer model It is a semiparametric interpolation technique which estimates the unknown information at one point according to the known information [21]. To estimate the stochastic process z(x), assuming that the true response surface of Kriging model is continuous, any two points will tend to have the same value as the distance approaches zero and it is the same for z(x) of two points. E likelihood function of the sample point can be expressed as (Y − Fβ)TR−1(Y − Fβ). Substituting equation (6) and equation (7) in equation (5) and ignoring the constant term, the logarithmic form of the maximum likelihood function can be expressed as ln(L) ≈ − n ln􏼐σ􏽢2􏼑 − 1 ln|R|. F R r(x) where rT(x0) is the row vector of correlation function between each sample point and the point x0 to be measured: rT x0􏼁 􏼂R x0, x1􏼁, R x0, x2􏼁, . . . , R x0, xn􏼁􏼃. (11)

Kriging-Based Model Updating Method

Numerical Example

Findings

Conclusions